Continuous Compound Interest

Demonstration of Various Compounding

The following table shows the final principal (P), after t = 1 year, of an account initally with C = $10000, at 6% interest rate, with the given compounding (n). As is shown, the method of compounding has little effect.

n

P

1 (yearly)

$ 10600.00

2 (semi-anually)

$ 10609.00

4 (quarterly)

$ 10613.64

12 (monthly)

$ 10616.78

52 (weekly)

$ 10618.00

365 (daily)

$ 10618.31

continuous

$ 10618.37

Loan Balance

Situation: A person initially borrows an amount A and
in return agrees to make n repayments per year,
each of an amount P.
While the person is repaying the loan, interest is accumulating
at an annual percentage rate of r, and this interest
is compounded
n times a year (along with each payment). Therefore, the person
must continue paying these installments of amount P until
the original amount and any accumulated interest is repayed.
This equation gives the amount B that the person still
needs to repay after t years.